Node-link-blob model

Several attempts have been made to relate these conductivity exponents tc or Sc with the percolation cluster statistical exponents discussed earlier. For example, in the node-link-blob model, the conductivity E of the network is proportional to the number of parallel links, while the... 

Using the node-link-blob model (see Section 1.2.1(d)) for the percolation cluster, one can in fact easily derive a rigorous bound of the fracture exponent Tf (Chakrabarti 1988, Ray and Chakrabarti 1988). This derivation is given below. One can see there that the above estimate for Tf in (3.12) turns out to be its lower bound. 

Fig. 1.3. A portion of the node-link-blob superlattice model for p > Pc-The distance between two nodes of the lattice (say A and B) is while the chemical length of the tortuous bond of the superlattice is Lc.

Several performance characteristics of rubber such as abrasion resistance, pendulum rebound, Mooney viscosity, modulus, Taber die swell, and rheological properties can be modeled by Eq 7.34. " A complex mathematical model, called links-nodes-blobs was also developed and experimentally tested to express the properties of a filled rubber network system. Blobs are the filler aggregates, nodes are crosslinks and links are interconnecting chains. The model not only allows for... 

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